[Turkmath:7361] Seminer-Andrej Dujella (University of Zagreb)-Bilecik-16 Aralık

[Ilker Inam]

Değerli Liste Üyeleri,



Bilecik Şeyh Edebali Üniversitesi Fen Fakültesi Matematik Bölümü Cebir ve
Sayılar Teorisi Anabilim dalı öğretim üyeleri tarafından kurulan
“Bilecik Algebra & Number Theory (BANT)” grubu tarafından organize
edilen seminer serilerinin yeni konuşması* 13 Ocak 2026 Salı günü* online
olarak zoom üzerinden düzenlenecektir.


Etkinliğin web sitesi: https://bilecikalgebranumbertheory.github.io/ dir.



Sıradaki konuşmacı Zagreb Üniversitesi'nin (Hırvatistan) değerli öğretim
üyesi* Andrej Dujella* olacaktır ve konuşma bilgileri aşağıda yer
almaktadır.



*Konuşma Adı:*  *Diophantine m-tuples and elliptic curves*

*Özet:* In this talk, we will describe some connections between Diophantine
m-tuples and elliptic curves. A rational Diophantine m-tuple is a set of m
nonzero rationals such that the product of any two of them, increased by 1,
is a perfect square. The first rational Diophantine quadruple was found by
Diophantus. It is known that there are infinitely many Diophantine
quadruples in integers (the first example, the set {1,3,8,120}, was found
by Fermat), and He, Togbe and Ziegler proved recently that there are no
Diophantine quintuples in integers. Euler proved that there are infinitely
many rational Diophantine quintuples. In 1999, Gibbs found the first
example of a rational Diophantine sextuple. It is still an open question
whether there exists any rational Diophantine septuple. We will describe
several constructions of infinite families of rational Diophantine
sextuples (this is joint work with M. Kazalicki, M. Mikic, V. Petricevic
and M. Szikszai). These constructions use properties of corresponding
elliptic curves. We will also show how Diophantine m-tuples can be used in
the construction of high-rank elliptic curves over Q and Q(t) with a given
torsion group (this is joint work with J. Aguirre and J. C. Peral). We will
also mention some of the open problems related to these topics.


*Tarih: 13/01/2026 *

*Saat: 16:00 İstanbul / 14:00 Berlin / 13:00 Londra / 22:00 Tokyo / 08:00
New York / 00:00 Sydney(+1)*



Katılım için linkte yer alan formun doldurulması yeterlidir,

Form linki: https://forms.gle/xaJ2uPTtvzxD6cTx9


Zoom linki formu doldurduktan sonra email ile paylaşılacaktır. Etkinlik
posteri ekte yer almaktadır.



Saygılarımla,

Prof.Dr. İlker İnam

Düzenleme komitesi adına.





—————————————————————



Dear list members,



The "Bilecik Algebra & Number Theory (BANT)" group, founded by the faculty
members of the Department of Algebra and Number Theory at Bilecik Seyh
Edebali University's Faculty of Science, will host its next semester on *Tue,
Jan 13, 2026*. The event will be conducted online via Zoom.

The website for the event is:  https://bilecikalgebranumbertheory.github.io/
.



The inaugural speaker will be *Andrej Dujella*, a faculty member at the
University of Zagreb, Croatia. Details of the presentation are provided
below.



*Title: **Diophantine m-tuples and elliptic curves*

*Abstract: *In this talk, we will describe some connections between Diophantine
m-tuples and elliptic curves. A rational Diophantine m-tuple is a set of m
nonzero rationals such that the product of any two of them, increased by 1,
is a perfect square. The first rational Diophantine quadruple was found by
Diophantus. It is known that there are infinitely many Diophantine
quadruples in integers (the first example, the set {1,3,8,120}, was found
by Fermat), and He, Togbe and Ziegler proved recently that there are no
Diophantine quintuples in integers. Euler proved that there are infinitely
many rational Diophantine quintuples. In 1999, Gibbs found the first
example of a rational Diophantine sextuple. It is still an open question
whether there exists any rational Diophantine septuple. We will describe
several constructions of infinite families of rational Diophantine
sextuples (this is joint work with M. Kazalicki, M. Mikic, V. Petricevic
and M. Szikszai). These constructions use properties of corresponding
elliptic curves. We will also show how Diophantine m-tuples can be used in
the construction of high-rank elliptic curves over Q and Q(t) with a given
torsion group (this is joint work with J. Aguirre and J. C. Peral). We will
also mention some of the open problems related to these topics.


*Date: Jan 13, 2026, Tuesday*

*Time: **16:00 İstanbul / 14:00 Berlin / 13:00 Londra / 22:00 Tokyo / 08:00
New York / 00:00 Sydney(+1)*



To participate, simply fill out the form at the following link:

Form Link: https://forms.gle/xaJ2uPTtvzxD6cTx9



The Zoom link will be shared via email after filling out the form. The
event poster is attached.



Best regards,

Prof.Dr. Ilker Inam

On behalf of the organizing committee
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